Vector Algebra Formulas - Mathematics Class 12

Learn important formulas from the Vector Algebra chapter of Class 12 Mathematics with examples, variables and applications.

📐 Vector Algebra Formulas

Complete collection of formulas with explanations and examples

Cross Product Magnitude

$$|a x b| = |a||b| sin theta$$

Description: Cross Product Magnitude is a standard relation used in vector-algebra.

Example:

Apply the relation: |a x b| = |a||b| sin theta

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.
  • Exam relevance: jee-main, jee-advanced, cuet

Dot Product

$$a dot b = |a||b| cos theta$$

Description: Dot Product is a standard relation used in vector-algebra.

Example:

Apply the relation: a dot b = |a||b| cos theta

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.
  • Exam relevance: jee-main, jee-advanced, cuet

Quick Reference

Cross Product Magnitude: $|a x b| = |a||b| sin theta$
Dot Product: $a dot b = |a||b| cos theta$

💡 Worked Examples

Step-by-step solutions using Vector Algebra formulas

Example 1: Solving Quadratic Equation

Quadratic Formula
Problem:

Solve: 2x² + 5x + 3 = 0

Solution:
  1. Identify coefficients: a = 2, b = 5, c = 3
  2. Apply quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
  3. Calculate discriminant: Δ = 5² - 4(2)(3) = 25 - 24 = 1
  4. Substitute values: x = (-5 ± √1) / 4 = (-5 ± 1) / 4
  5. Find roots: x₁ = (-5 + 1)/4 = -1, x₂ = (-5 - 1)/4 = -3/2
Answer:

x = -1 or x = -3/2

Example 2: Arithmetic Progression Sum

AP Sum Formula
Problem:

Find the sum of first 10 terms of AP: 2, 5, 8, 11, ...

Solution:
  1. Identify: a = 2 (first term), d = 3 (common difference), n = 10
  2. Apply formula: Sₙ = n/2[2a + (n-1)d]
  3. Substitute: S₁₀ = 10/2[2(2) + (10-1)(3)]
  4. Simplify: S₁₀ = 5[4 + 9(3)] = 5[4 + 27] = 5(31)
  5. Calculate: S₁₀ = 155
Answer:

Sum = 155

🎯 Practice Problems

Try these problems to test your understanding:

Practice Problem 1

Solve the quadratic equation: x² - 7x + 12 = 0

Practice Problem 2

Find the area of a circle with diameter 14 cm.

Practice Problems

Check Your Formula Recall

Write each formula once, define every variable, then solve one direct substitution problem before moving to mixed questions.

Apply Vector Algebra

Pick two formulas from this page and create your own values for the variables. Verify units and signs before calculating.

Derivation Notes

Focus on how the formula is built, not only the final expression. Derivations help with board-exam reasoning and multi-step application questions.

  • Start from the definition or identity used in the chapter.
  • Write assumptions clearly before substituting values.
  • Track units through each step to catch calculation mistakes.

Where These Formulas Are Used

Board Exam Problems

Use these formulas for direct numerical questions, proof-based steps, and short-answer reasoning in Mathematics.

Competitive Practice

Memorize the condition of use for each formula so you can identify the right expression quickly under timed practice.

Related Formula Chapters

Applications Of Derivatives 1 formulas Applications Of Integrals 1 formulas Continuity And Differentiability 2 formulas Determinants 1 formulas Differential Equations 1 formulas Integrals 2 formulas Inverse Trigonometric Functions 1 formulas Matrices 1 formulas Probability 1 formulas Relations And Functions 1 formulas Three Dimensional Geometry 1 formulas Vector Algebra 2 formulas

These Vector Algebra formulas help students revise concepts quickly and apply equations accurately in exam-style problems.

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